High Performance Arithmetic for Hyperelliptic Curve Cryptosystems of Genus Two

Jan Pelzl, Thomas Wollinger, Chris­tof Paar

International Conference on Information Technology: Coding and Computing - ITCC, Las Vegas, Nevada, USA, April 5-7, 2004.


Abstract

Regarding the overall speed and power consumption, cryptographic applications in embedded environments like PDAs or mobile communication devices can bene?t from specially designed cryptosystems with ?xed parameters. In this contribution, we propose a highly ef?cient algorithmfor a hyperelliptic curve cryptosystem (HECC) of genus two, well suited for these applications on constrained devices. This work presents a major improvement of HECC arithmetic for certain non-supersingular curves de?ned over ?elds of characteristic two. We optimized the group doubling operation and managed to speed up the whole cryptosystem by approximately 27% compared to the previously known most ef?cient case. Furthermore, an actual implementation of the new formulae on an embedded processor shows its practical relevance. A scalar multiplication can be performed in approximately 50 on an 80MHz embedded device.

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